Question

Use the substitution method to solve the system x=y−4
, x+8y=2
.

Answer 1

To solve the system of equations using the substitution method, we start with the given equations:

1. \( x = y - 4 \) (Equation 1)
2. \( x + 8y = 2 \) (Equation 2)

We'll substitute Equation 1 into Equation 2.

### Step 1: Substitute Equation 1 into Equation 2

Replace \( x \) in Equation 2 with \( y - 4 \):

\[
(y - 4) + 8y = 2
\]

### Step 2: Simplify the equation

Combine like terms:

\[
y - 4 + 8y = 2
\]

\[
9y - 4 = 2
\]

### Step 3: Solve for \( y \)

Add 4 to both sides:

\[
9y = 6
\]

Now, divide both sides by 9:

\[
y = \frac{6}{9} = \frac{2}{3}
\]

### Step 4: Substitute \( y \) back into Equation 1 to find \( x \)

Now that we have \( y \), we substitute it back into Equation 1 to find \( x \):

\[
x = y - 4
\]

\[
x = \frac{2}{3} - 4
\]

Convert 4 into a fraction with a denominator of 3:

\[
x = \frac{2}{3} - \frac{12}{3}
\]

\[
x = \frac{2 - 12}{3} = \frac{-10}{3}
\]

### Final Solution

Thus, the solution to the system of equations is:

\[
(x, y) = \left( -\frac{10}{3}, \frac{2}{3} \right)
\]